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A general model of processing stimuli suggests that when information does not provide informational value, then we gradually begin to ignore it. Such a model is consistent with the experience of many people in relation to background traffic noise when moving from a quiet to a noisy neighbourhood. I.e., the frequency with which external traffic noise enters into personal awareness gradually decreases over time.

Habituation to traffic noise while sleeping

Kawada (1995) provides a review of the effect of traffic noise on sleep. Specifically in relation to habituation the author wrote:

Habituation to noise: Views and opinions on this parameter differ. Thiessen et al. reported habituation to intermittent
wakefulness10～12. In their study, subjects were exposed to passing
truck noise less than 20 times a night with a peak level of 65 dBA.
The probability of a shift to shallower sleep and the amount of deep
sleep demonstrated failure of adaptation over 24 successive nights.
The probability of awakening decreased by almost one half in two
weeks. Griefahn also studied habituation of 36 students to
high-density road traffic noise and detected an all-night effect of
noise on sleep for 12 consecutive nights13. Deep sleep was prolonged
and shallow sleep including intermittent wakefulness became
progressively shorter at 37 to 63.5 dBA. Vallet at al. indicate that
there is no habituation to noise14. According to experiments on
subjects living in a noisy environment for more than four years,
young subjects showed less deep sleep and older subjects, less REM
sleep under conditions of silence. Both Di Nisi et al. and Ohrstrom
reported that there seems to be no habituation to noise
exposure15,16. They exposed subjects to randomly distributed noise
and it was impossible to predict either the time of exposure or the
type of noise presented. Kawada and Suzuki could find no definite
habituation to a noisy environment17. Their interval of noise
exposure was 15 minutes and there was only one pattern of passing
truck noise. Essentially the same noise characteristics are reported
by Thiessen, but the findings differed from each other. Based on
inter-individual variation in sensitivity to noise, habituation
should differ according to the person.

I find this summary a little confusing. The between subject studies are not especially relevant in that habituation should presumably reduce the disruption caused by noise, but not necessarily remove the effect. Thus, it seems like longitudinal evidence would be the most relevant.

General review of noise on sleep

Muzet (2007) provides a relatively recent review of research on the effects of environmental noise on sleep.
With regards to habituation the author wrote:

[Autonomic responses, such as heart rate changes and vasoconstrictions
in response to noise while sleeping] have bee found not to habituate
over long exposure times compared with clear subjective habituation
over successive noise-exposed nights.

Research on alarm clocks

I found an article by Moorcroft et al (1997) that discussed the role of alarm clocks in peoples awakening process

The ability to awaken oneself from sleep at a preselected time without
external means (such as alarm clocks) was studied using, first,
subjective and, second, objective methods. First, in a telephone
survey of 269 unselected adults, over one-half said that they never
use an alarm clock (or other external means) or always awaken before
it. Another 24% said that they sometimes awaken before the alarm.
Furthermore, this ability positively correlated with age and was
related to consistency in the amount of nightly sleep but not
consistency in wake-up time. Second, 15 people who said they regularly
self-awaken were objectively tested for this ability in their own beds
using actigraphy for three consecutive nights while choosing their own
wake-up times. Five awoke within 10 minutes of their target time
(mostly before) on each night, five did so on two of the three nights,
and of the remaining five, four did so on one night. Choice of target
times varied considerably within subjects but more so for those who
were more successful. Taken together these results show that many
people have the ability to regularly awaken themselves from sleep at a
desired time and that such an ability is of practicable utility.

Does having a consistent alarm clock decrease ability to wake up

I haven't found any specific empirical data on your question.

Habituation processes would suggest that a consistent noise that is deemed to carry a lack of informational content will gradually be more frequently ignored, and thus an inconsistent noise may be more effective in generating attention and perhaps wakefulness. That said, alarm clocks do carry informational content, and people could potentially tune themselves to that noise as the important noise to indicate the time to wake up.